Adam and Bryan have a total of $114.
Adam spends
14 of his money and
Bryan spends
16 of his money.
They spend $22 altogether.
- How much does Adam have at first?
- How much does Bryan have in the end?
|
Adam |
Bryan |
Before |
4 u |
6 p |
Change |
- 1 u |
- 1 p |
After |
3 u |
5 p |
(a)
Amount that Adam has at first = 4 u
Amount that Bryan has at first = 6 p
Total amount that they have = 4 u + 6 p = 114 --- (1)
Total amount that they spend = 1 u + 1 p = 22 --- (2)
(2)
x 6 6 u + 6 p = 132 --- (3)
(3) - (1)
(6 u + 6 p) - (4 u + 6 p) = 132 - 114
6 u + 6 p - 4 u - 6 p = 132 - 114
6 u - 4 u + 6 p - 6 p = 18
6 u - 4 u = 18
2 u = 18
1 u = 18 ÷ 2 = 9
Substitute 1 u = 9 into (1).
4 u + 6 p = 114
4 x 9 + 6 p = 114
36 + 6 p = 114
6 p = 114 - 36 = 78
1 p = 78 ÷ 6 = 13
Amount that Adam has at first
= 4 u
= 4 x 9
= $36
(b)
Amount that Bryan has in the end
= 6 p - 1 p
= 5 p
= 5 x 13
= $65
Answer(s): (a) $36; (b) $65